The vector equation of a line passing through a point with position vector and perpendicular to two lines with vector equations = + λ and = + λ, is given by = + λ() because as we know that vector product between two vectors will give you a vector whose direction is perpendicular to both the vectors, so the required equation is parallel to this vector and hence this is the equation.

Now we are given with,

= (+–3) and the lines perpendicular to required line are,

= +λ(2+–3) and = (2+)+μ(++)

= 2+–3 and = ++

Now,

=

=

=

Therefore, the required equation is,

= +–3 + ρ(4–5+)